Rei\ 0. Fisher — On Faulting, Jointing and Cleavage. 213 



force, for it is only by it that any lofty prismatic column of masonry 



can stand. Nevertheless, there would be a limiting height to any 



such a column, and that will no doubt be exceeded by the depth of 



cover in such cases as we are considering. 



We have then the two limiting angles 9 given by the relation 



2«, 

 sin 2 6=^-^ between which the shearing force is sufficiently great to 



cause separation. 



The second condition requisite is that motion can take place. 

 In order that faulting along A JB may be possible, we must have 

 the force along A B greater than the friction ; or, if v be the coeffi- 

 cient of friction, it must not be less than v x the pressure on A B. 



Now it is easily seen that, in the general case, the pressure on 

 A B will be equal to, 



W cos- dJ^P sin^ 9, . 

 or in the present instance to W cos- 9. Therefore we must have 

 W sin 9 cos 9 = V. W cos^ 9. 

 or tan 9 = v. 



In other words, the hade of the fault surface cannot be less than 

 the angle of repose. 



The choice of the angle of hade will evidently depend upon the 

 shearing force, and the friction, conjointly. At a given depth the 

 shearing force \ W sin 2 9, will be greatest when 9 = 45°. In that 

 case ^ W = ju; and any smaller value would render sin 29 impossible. 



Hence, if the angle of repose is less than 45°, the hade of the fault 

 surface will be 45°. But, if the angle of repose is greater than 45°, 

 the hade will be the angle of repose, provided it lie within I in. 

 But if it do not, faulting cannot be induced. 



It seems however, that the considerations connected with room 

 for motion, may come into play in determining the hade between 

 the possible limits within the angle I m. And faults with different 

 hades will be formed subsequently to one another, during the pro- 

 cess of contraction. They would intersect one another, and the 

 faults of steepest hade might be expected to be formed before those of 

 less steep hade, because the tendency to gape would increase more 

 at the upper part of the cracks than at the lower as time went on. 



We have considered the disturbances as if they took place only in 

 one direction, say E. and W. Those in the orthogonal, N. and S., 

 will be governed by similar laws. But it will be observed that, 

 whereas the tension P in one of these directions will be wholly 

 independent of that in the other, yet the weight of rock, which gives 

 rise to W, is unique. Consequently that part of the potential energy 

 of W which goes to form faults in one system, say E. and W., will 

 not be available to form them N. and S. There is no reason, except 

 accidental circumstances, to rule in which direction W shall be 

 chiefly operative. Hence, though the jointing will be probably as 

 strongly developed in one direction as in the other, the faulting will 

 probably be developed chiefly in one direction, and less pronounced 

 in that orthogonal to it. 



{To be continued.) 



